Above shows the network topology used for this demonstration.
RT1 is configured with a route map to set the MED for its locally originated routes in AS 65001 to 100.
The MED attribute only being exchanged between neighbors ASes and not be propagated further to downstream or upstream ASes. So RT3 won't be able to see the MED value for 192.168.1.0/24 originated from AS 65001.

hey, RT2 claims that it advertised the MED value for 192.168.1.0/24 to RT3.
WHAT!?! What I see is not what I really get!?! ~!@#$%^&*()

Conclusion:
The output of the show ip bgp neighbors {ip-addr} advertised-routes is actually displaying the routes in the Loc-RIB instead of the Adj-RIB-Out, which means that the routes that are yet to be processed by the output policy engine that performs the actions for manipulating routes, eg: MED, AS path prepending, etc. Period. :-)

So, this should be the way. :-)

Router#sh ip bgp neighbors 2.2.2.2 ?
advertised-routes Display the routes that are going to be advertised to a BGP neighbor
dampened-routes Display the dampened routes received from neighbor
flap-statistics Display flap statistics of the routes learned from
neighbor
paths Display AS paths learned from neighbor
received Display information received from a BGP neighbor
received-routes Display the received routes from neighbor
routes Display routes learned from neighbor
| Output modifiers
<cr>
Router#